Never Too Rigid to Reach: Adaptive Virtual Model Control with LLM- and Lyapunov-Based Reinforcement Learning

TL;DR

This paper introduces an adaptive control framework for robotic arms that combines Large Language Models and Lyapunov-based Reinforcement Learning to enhance stability, adaptability, and coordination in uncertain environments.

Contribution

It presents a novel integration of LLMs and Lyapunov RL into Virtual Model Control, enabling online adaptation with stability guarantees and improved task flexibility.

Findings

Achieves superior performance in dynamic tasks with a 7-DoF Panda arm.

Enhances virtual component coordination through LLM-guided structured priors.

Ensures safe adaptation via Lyapunov-based stability constraints.

Abstract

Robotic arms are increasingly deployed in uncertain environments, yet conventional control pipelines often become rigid and brittle when exposed to perturbations or incomplete information. Virtual Model Control (VMC) enables compliant behaviors by embedding virtual forces and mapping them into joint torques, but its reliance on fixed parameters and limited coordination among virtual components constrains adaptability and may undermine stability as task objectives evolve. To address these limitations, we propose Adaptive VMC with Large Language Model (LLM)- and Lyapunov-Based Reinforcement Learning (RL), which preserves the physical interpretability of VMC while supporting stability-guaranteed online adaptation. The LLM provides structured priors and high-level reasoning that enhance coordination among virtual components, improve sample efficiency, and facilitate flexible adjustment to varying task requirements. Complementarily, Lyapunov-based RL enforces theoretical stability constraints, ensuring safe and reliable adaptation under uncertainty. Extensive simulations on a 7-DoF Panda arm demonstrate that our approach effectively balances competing objectives in dynamic tasks, achieving superior performance while highlighting the synergistic benefits of LLM guidance and Lyapunov-constrained adaptation.